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Question
Find the values of p, q, r, and s if
`[("p"^2 - 1, 0, - 31 - "q"^3),(7, "r" + 1, 9),(- 2, 8, "s" - 1)] = [(1, 0, -4),(7, 3/2, 9),(-2, 8, -pi)]`
Solution
`[("p"^2 - 1, 0, - 31 - "q"^3),(7, "r" + 1, 9),(- 2, 8, "s" - 1)] = [(1, 0, -4),(7, 3/2, 9),(-2, 8, -pi)]`
Equating the corresponding entries
⇒ p2 – 1 = 1
⇒ p2 = 1 + 1 = 2
p = `+- sqrt(2)`
– 31 – q3 = -4
– q3 = – 4 + 31 = 27
q3 = – 27 = (– 3)3
⇒ q = – 3
r + 1 = `3/2`
⇒ r = `3/2 - 1 = (3 - 2)/2 = 1/2`
s – 1 = π
⇒ s = – π + 1
(i.e.,) s = 1 – π
So, p = `+- sqrt(2)`
q = – 3
r = `1/2` and s = 1 – π
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